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We calculate the partition functions of supersymmetric gauge theories on S^5,which acquire non-perturbative contributions from instanton loops wrapping itsHopf fiber. The instantons on the CP^2 base equivariantly localize to 3 fixedpoints of SU(3) Cartans. Using our results, we study the index of the 6d (2,0)theory. We first study the partition functions of maximal SYM with AD(E) gaugegroups, which agree with the gravity dual indices on AdS_7 in the large Nlimits. We also show that the most general partition function of the Abeliantheory agrees with the index for a free 6d tensor supermultiplet. We explainpossible ambiguities in our 5d approach, role of maximal SUSY, and the Wilsonloops on S^5 dual to M2-brane Wilson surfaces in AdS_7.

Instantons on the 5-sphere and M5-branes